A sequence of random variables {Xi} such that the expected value of the (n + 1)th random variable, once the first n outcomes are known, is just the current value Xn. The simple random walk, which moves left or right one step with probability 0.5, is an example of a martingale.
The sequence of random variables X1, X2,…(with finite expected values) is a martingale if the conditional expected value of Xn+1, given the values of X1, X2,…, Xn, is given by
An example is provided by letting Xn be the amount of a gambler's winnings after the nth of a sequence of fair games.
A stochastic process in which the expectation of the future value of a variable, conditional on currently available information, including the current value, is equal to the current value of the variable.
- Matthias, Bernd Teo
- Matthias I (1443–90)
- Mattingly, Thomas, II (1936– )
- Matura diamond
- maturation
- maturation-promoting factor
- maturity
- Matuyama
- Matuyama, Motonori
- Matuyama, Motonori (1884–1958)
- Mauchly test
- Maud
- Mau Mau
- Mauna Kea Observatories
- Maunder, Edward Walter
- Maunder, (Edward) Walter (1851–1928)
- Maunder minimum
- Maupertuis, Pierre-Louis Moreau de
- Maupertuis, Pierre‐Louis Moreau de (1698–1759)
- Mauritania
- Mauritius
- Mauryan empire
- Maury, Antonia Caetana de Paiva Pereira
- Maury, Matthew Fontaine
- Maury, Matthew Fontaine (1806–73)